Evans, G. B. A.; Savin, N. E. Testing for unit roots. II. (English) Zbl 0579.62014 Econometrica 52, 1241-1269 (1984). Summary: [For part I see ibid. 49, 753-779 (1981; Zbl 0468.62021).] This paper investigates the exact sampling distribution of the least squares estimator of \(\beta\) in the model \(y_ t=\mu +\beta y_{t- 1}+u_ t\) where the \(u_ t\) are independently \(N(0,\sigma^ 2)\). The distribution is calculated for the case where \(y_ 0\) is a known constant and where \(y_ 0\) is a random variable. Given \(y_ 0\) is a constant we prove a small \(\sigma\) asymptotic result and compute the exact powers of nonsimilar tests of the random-walk hypothesis \(\beta =1\) and of the stability hypothesis \(\beta =0.9\). The exact powers of a test of the stability hypothesis are calculated for the case where \(y_ 0\) is random. The accuracy of the standard normal approximation is examined for both start-up regimes. Cited in 1 ReviewCited in 41 Documents MSC: 62E15 Exact distribution theory in statistics 62P20 Applications of statistics to economics 62F03 Parametric hypothesis testing Keywords:testing for unit roots; first order autoregressive process; tables; ordinary least squares; least squares estimator; exact powers; random- walk hypothesis; stability hypothesis; standard normal approximation Citations:Zbl 0468.62021 PDFBibTeX XMLCite \textit{G. B. A. Evans} and \textit{N. E. Savin}, Econometrica 52, 1241--1269 (1984; Zbl 0579.62014) Full Text: DOI